subspaces of R^3 are lines and planes through the origin
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Determine which subsets given below are subspace of R^3
1) {x l x_1 greater or equal to 0}
2) {x l x_1=0}
3) {x l x_1+x_2+x_3=1}
4) {x l x_1+x_2+x_3=0}
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Solution Summary
This tutorial expresses how subspaces of R^3 are lines and planes through the origin.
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In general, subspaces of R^3 are lines and planes through the origin.
1) {x l x_1 greater or equal to 0}
This is not a subspace because it is not closed under additive inverses. For instance, (1,0,0) is in the set but (-1,0,0) is not.
2) {x l x_1=0}
This is ...
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